Improved regula falsi method for solving the Schrödinger equation with a piecewise constant potential

1987 ◽  
Vol 68 (1) ◽  
pp. 180-187
Author(s):  
M Friedman ◽  
A Rabinovitch
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Piecewise Constant ◽  
Constant Potential ◽  
Regula Falsi Method

scholarly journals The time-dependent Schrödinger equation with piecewise constant potentials

2018 ◽  
Vol 31 (1) ◽  
pp. 57-83
Author(s):  
NATALIE E. SHEILS ◽  
BERNARD DECONINCK
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Spatial Dimension ◽  
Time Dependent ◽  
Interface Problems ◽  
Solvable Models ◽  
Transform Method ◽  
Piecewise Constant ◽  
Constant Potential ◽  
Time Dependent Problem

The linear Schrödinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with physically important models. In examples such as ‘particle in a box’ and tunnelling, attention is restricted to the time-independent Schrödinger equation. This paper combines the unified transform method and recent insights for interface problems to present fully explicit solutions for the time-dependent problem.

scholarly journals RECONSTRUCTION ALGORITHMS OF AN INVERSE COEFFICIENT IDENTIFICATION PROBLEM FOR THE SCHRODINGER EQUATION

2017 ◽  
Vol 22 (3) ◽  
pp. 352-372
Author(s):  
Ji-Chuan Liu
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Identification Problem ◽  
Observation Data ◽  
Reconstruction Algorithms ◽  
Piecewise Constant ◽  
Coefficient Identification ◽  
Ill Posed ◽  
Inverse Coefficient

In this paper, we consider an inverse problem of coefficient identification for the Schrodinger equation from the observation data on the exterior boundary. Our aim is to detect the number, the location, the size and the shape of the coefficient with piecewise constant within a body. This problem is nonlinear and ill-posed, thus we should apply stable and elegant reconstruction algorithms in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods.

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